There are many applications, like road construction and agriculture, where a vehicle is automatically steered along a target path. At the current level of road construction technology, the positioning accuracy expected of working tools or implements may be several millimeters. To increase planting density in agriculture and to save water and fertilizer, agricultural implements should have a position accuracy level of a centimeter. These and other similar tasks are performed by wheeled robotized vehicles equipped with satellite and inertial navigation tools and controllers, which provide automatic steering along a predefined path.
Nevertheless, control of such a wheeled robot does not exclude manual steering. Presence of an operator is necessary for safety considerations, e.g., in the case where the vehicle meets an unexpected obstacle. Another, even more significant reason to switch to manual control is when the closed loop control system loses stability due to unexpected disturbances in the sensors, which takes the system out of the stability region. For these reasons, an unmanned vehicle cannot be guaranteed to stay on the predefined path and provide stable tracking using sensors alone, such as GNSS and inertial sensors.
Generally speaking, two kinds of problems arise in automatic control of wheeled vehicles: (1) planning of a target path and (2) automatic driving of the vehicle to the target path and stabilizing the motion along it. The first problem of planning a target path arises from the type of construction or agricultural task. The second problem is usually solved by synthesizing a control law that stabilizes the motion of the vehicle along the target path, the control law obtained when solving the first problem.
However, the control law obtained from planning a target path does not provide global stability. In studies of stability and attraction domain, state space representation is usually used. In the case of a wheeled robot, the state space vector is usually given by position, orientation, and steered wheel angle. Automatic driving along the target path is not guaranteed if the system starts from an initial state not belonging to the attraction domain in the state space. As a result, driving the vehicle into the attraction domain can be performed either manually or using another algorithm that differs from the control law. The vehicle must be equipped with a special indicator on the control panel to let the operator know when it is safe to switch to automatic control. If the system estimates its state as belonging to the attraction domain, the system switches the indicator lamp to a green light. Otherwise, if the system estimates its state as not belonging to the attraction domain, the indicator lamp is switched to a red light to signal to the operator that switching to automatic control may not be safe. The red light indicates that transient processes are unpredictable and asymptotic stability may be not guaranteed. More specifically, exponential rate of convergence may not be guaranteed. Hence, it follows that estimation of the attraction domain is important to establish safety of automatic control of robotic wheeled vehicles.
Thus, it would be beneficial to have an apparatus and method for the efficient control of safety indicators based on numerically efficient estimation of the attraction domain. It is clear that different applications demand different approaches to estimation, or even for definition of the attraction domains.